When mining with a room-and-pillar method, the urgent task is to estimate the critical state of interchamber pillars. An effective control method is to measure the horizontal convergence rate of stopes.

Physical modelling of the interchamber pillar fracture was carried out by uniaxial loading of salt specimens with a control of longitudinal and transverse deformations. Three-dimensional modelling was carried out by the finite element method in an elastoplastic statement considering the hardening effect. The solution region was divided into the first order isoparametric elements of the hexahedral shape. The solution of the incremental nonlinear finite element equations was carried out according to the modified Newton-Raphson scheme. For the numerical integration of plastic constitutive equations, an implicit scheme of return-mapping algorithm was used. A three-dimensional modification of the Botkin and Mirolubov strength criterion was adopted as a yield criterion. Calibration of the model was carried out according to the results of laboratory tests for the fracture of salt specimens of a cubic form.

The resulting mathematical model of fracture quite closely describes the experimental data: loading curve and distribution curves of transverse deformations over the specimen's cross section. Some differences between model and experimental data were revealed.

1 Introduction

As part of the study of the deformation processes of the bearing elements of the room-and-pillar system at the Verkhnekamsk potash deposit, a number of full-scale and laboratory studies of the salt deformation process were carried out. One of the test run aimed at evaluating the deformation rates and determining the correlation of the longitudinal and transverse deformations of interchamber pillars included an experiment on uniaxial compression of large cubic specimens of saliferous rocks with control of longitudinal and transverse deformations. Such an experiment was carried out in laboratory conditions (Fig. 1). The control of specimen's deformations was performed using a system of deep and contour marks. The displacements of marks were recorded by observing a non-contact three-dimensional optical system that simulates the use of an extensometer on the specimen's surface. The experiment resulted in an average curve of the longitudinal load dependence on the longitudinal deformation (Fig. 2), as well as the transverse deformation distribution over the specimen's cross section (Fig. 3). The graph of the averaged loading curve shows that there are two modes of specimen deformation: elastic (up to about 1500 kN) and plastic (over 1500 kN). Conversely, transverse deformation diagrams show an essentially linear dependence throughout the entire deformation process. In this paper, a theoretical description of the obtained loading curve and distribution curves of transverse deformations is carried out using the rock strength criterion proposed in the work (Baryakh A.A. and Samodelkina N.A. 2017).

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